Hunting a light CP-violating Higgs via diffraction at the LHC

We study the central diffractive production of the (three neutral) Higgs bosons, with a rapidity gap on either side, in an MSSM scenario with CP-violation. We consider the bb-bar and tautau-bar decay for the light H_1 boson and the four b-jet final state for the heavy H_2 and H_3 bosons, and discuss the corresponding backgrounds. A direct indication of the existence of CP-violation can come from the observation of either an azimuthal asymmetry in the angular distribution of the tagged forward protons (for the exclusive pp -> p+H+p process) or of a sin(2phi) contribution in the azimuthal correlation between the transverse energy flows in the proton fragmentation regions for the process with the diffractive dissociation of both incoming protons (pp -> X+H+Y). We emphasise the advantage of reactions with the rapidity gaps (that is production by the pomeron-pomeron fusion) to probe CP parity and to determine the quantum numbers of the produced central object.